[PairTheBoard]

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Hey PTB,

you said: "I agree with your friend and his colleague under the assumption that the amounts in the envelopes are Fixed."

COnsider the following. If I made 100 pairs of envelopes with variable ammounts, such that each pair of envelopes contains N and 2N values. We play the game. You choose an envelope at random. And you then switch blind, or you don't. Would you predict that now switching affects EV?

Also would you think that your EV would be affected if now after picking an envelope you are now shown the value that ethe envelope contained?

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No and No.

You ask, where does argument 1 break down? It's in the conclusion once seeing the amount A in Env 1, that chances are 50-50 that Env 2 has 2A. With Fixed envelope amounts the chances are either 0% or 100% you just don't know which. That's the principle that negates argument 1. If the amounts come from a population of 100 envelope pairs - or some other unknown probabilty distribution - then the conditional probabilty that Env 2 has 2A is still something other than 50% in general, and just like above you don't know what it is. It's the same principle negating argument 1. The principle is just more apparent in the Fixed Amount case.

PairTheBoard